{"id":"openai-math/Sharp-One-Third-Stability-of-Brenier-Maps","pdf":"https://github.com/openai/math/blob/main/preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026/article.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharp-One-Third-Stability-of-Brenier-Maps-September-25-2026","tags":["optimal-transport","stability","convex-geometry"],"score":0,"title":"Sharp One-Third Stability of Brenier Maps","domain":"Partial differential equations","family":"374","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"For the uniform probability measure ρ on a compact convex body in ℝ d , d ≥ 2, quadratic optimal transport maps are one-third Hölder continuous in $`L^2(\\rho)`$ with respect to the target's 2-Wasserstein distance. The constant is uniform over all targets supported in a fixed compact set, and the exponent is optimal. A three-atom family on a fixed cube disproves Letrouit's conjectured uniform square-root estimate.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Sharp one-third stability of Brenier maps"}